Blog – Jason H. Nicholson

Newton basin-of-attraction plot with the fixed-point step.

Newton step driven by Fixed Point Theorem

math

programming

In Trust-Region-Dogleg and Newton-Raphson - A Quick Comparison on a 5th order polynomial, we saw how the Newton-Raphson method produces a fractal pattern in the complex…

Reference to World’s Toughest Mudder 2016: A Cautionary Tale

running

endurance

obstacle-course-racing

ultramarathon

mudder

I resurrected this post from 2016 because it is still relevant today. I converted it from a docx file to markdown, added some more pictures, updated grammar/clarity, and…

FFMetrics

video

VMAF (Video Multi-Method Assessment Fusion) is a perceptual video quality metric developed by Netflix that combines multiple quality metrics to provide a single score that…

When Turning OSQP Scaling Off Wins on a Constrained Least-Squares QP

optimization

MATLAB

I recently worked through a constrained least-squares problem where my intuition was wrong: OSQP solved faster and more reliably with internal scaling turned off.

Comparing AI Models on MATLAB Code Conversion: Madsen-Reid Results

AI

MATLAB

WIth GitHub Copilot’s recent announcement of “usage billing”, I decided it was important to understand the AI API usage landscape better. I bought some API credits and ran a…

Running Fork (Windows) on Linux with Wine

git

wine

linux

developer-tools

Fork is a fast, polished Git GUI available for Windows and macOS — but not Linux. This post documents how to run Fork 2.16.1 on Linux under Wine, including binary patches…

Jason H. Nicholson

Solving Sparse Normal Equations: ichol+PCG, Laplacians.jl, and Spectral Preconditioners

math

programming

I solve large sparse normal equations of the form \(A^T A \, x = A^T b\) where \(A\) is built by stacking a fidelity (interpolation) matrix and scaled 2nd-derivative finite…

Linear Least Squares to Quadratic Program

math

This is the derivation from a constrained linear least squares problem to a quadratic program.

Integrating Jupyter, MATLAB, and Quarto in VS Code

devOps

programming

If you like notebooks for exploration but also want clean, publishable technical writing, this stack works very well:

Summary of a second order cavitation model

CFD

math

This post was AI generated to help summarize the key aspects of a second-order cavitation model proposed by (Liu et al. 2026). My quick take is this is more advanced model…

The full cavitation model with only NCG (no vapor)

CFD

math

This note takes the Singhal et al. (2002) homogeneous-mixture framework and explicitly turns off the vapor/cavitation part (no vapor phase, no phase change). What remains is…

Summary of the full cavitation model

CFD

math

This post is a code-oriented restatement of the Full Cavitation Model from Singhal et al. (2002), with the core equations collected in one place.

Jake’s command line tools

devOps

I have a coworker named Jake who is a big fan of command line tools. Here some of the tools has recommended and I am learning. Below is a list of tools he recommended.

Understanding how damping ratio affects the poles of a second order system

controls

math

In simulation and controls, its important to understand the details of a second order system. This post is how the damping ratio affect the poles of a second order system.

CAE Workstation setup

CAE

computing

Re-encoding a Google photo/video album

programming

video

One common issue is running out of space on your smartphone or in the cloud because of photos and videos. Google provides “storage saver” settings that help, but they don’t…

Encoding many videos with ffmpeg, handbrake, and nvencc

computing

programming

video

I was working figure out the best combination of settings for ffmpeg, handbrake, and nvencc to encode a large number of videos. I wanted to compare the quality and file size…

Setting up a website and email - DNS, GitHub, Markdown

devOps

computing

I recently migrated away from BlueHost and WordPress to a static site generator using GitHub Pages and Quarto. I moved my email from Bluehost to purelymail.com.The process…

Switching to Quarto from Franklin.jl

devOps

programming

After initially migrating to Franklin.jl in the last several weeks, I migrated again to Quarto. Franklin.jl is okay but Quarto is better. Here are my reasons migrating:

Converting a docx to md - Math, tables, and html

programming

I used pandoc to convert a word file to .md.

Setting Up a Franklin.jl Blog

devOps

UPDATE 2025-11-28: I migrated to Quarto because of issues like the one below.

Engineering Workstation Build

CAE

computing

The main goal of this build is to make a custom engineering workstation that is appropriate for Scientific Computing (MATLAB), CAD (SolidWorks, OnShape, AutoDesk products…

Trust-Region-Dogleg and Newton-Raphson - A Quick Comparison on a 5th order polynomial

math

programming

A Newton-Raphson iteration produces a fractal pattern in the complex plane and a Trust-Region-Dogleg method produces a smoother pattern in the complex which is desirable for…

Neural Networks. Controls, and System Identification

system-identification

controls

The current engineer atmosphere is buzzing about Neural Networks. The downside is that Neural Networks do not have a structure that is easily understandable and…

System Identification Resources

controls

system-identification

This blog post was turned into a page here: System Identification Resources

Linux HTML Documentation Index

devOps

computing

On Ubuntu Linux, there is a package called “dhelp”. dhelp allows viewing the man and info pages through a web browser. I find this very useful. man2html and info2www are…

Nonlinear Equation System Solving Using Newton, Line Search, and LU factorization

math

A couple of weeks ago, I was inspired to revisit Newton’s method for solving nonlinear equations. I was reminded of my undergrad days when I read a paper by Madsen and Reid…

SSH, Windows, Web Servers, Linux, and Visual Studio Code

devOps

programming

The hardest thing about trying to do something new with computers these days is that it is hard to focus on the one new thing I am trying to learn. I want to start working…

Object-Oriented Programming Decline - The Rise of other Paradigms

programming

I listen to a lot of computer science-related talks and podcasts. Recently, I have seen a trend away from the object-oriented paradigm. The premise is fusing your data and…

Time and Quality Work

misc

The more time you put into something, generally the higher the quality.

Reverse Engineering a Graph

misc

Sometimes you need data from a graph. WebPlotDigitizer is one way you can extract the data in an automated way. Check out the video below.

Using the Shortname

programming

The Shortname is a Windows way of dealing with non-ASCII characters and long file names and paths.

FFmpeg, The -crf Option, iPhone Videos, and Corporate Networks

computing

programming

I use FFmpeg on a regular basis for video, audio, and image-related editing. It is a command-line tool that goes from very simple to very complicated. I intend to stick with…

Short and Long Name VBA Functions

programming

From time to time I write VBA. One of the things I have needed is what is called the short path. If you ever worked at the command line, it looks like what is shown below.…

How to Export Your VBA Macros for Storage in a GIT/SVN Repository

devOps

programming

This shows a quick workflow I use to handle VBA Macros so that they are diffed properly in a GIT/SVN repository.

NASA T-MATS

CAE

An open source thermodynamic modeling package completed on behalf of NASA. The Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS) package offers a…

Comprehensive List of Lumped Parameter Simulation Software

simulation

Comprehensive List of Lumped Parameter Simulation Software

CAELinux

CAE

devOps

computing

If you haven’t seen CAELinux, then I highly recommend it. There is a lot of CAE software available in a single Ubuntu Linux based distro.

CFD, FEA, and Multiphysics Simulation

CFD

FEA

CAE

simulation

I have been working on learning the Deal.ii library. Why? Because it is one of the most advanced finite element libraries I have come across. It can handle adaptive mesh…

Piston Rings Multiphysics Simulation

FEA

CAE

simulation

My main goal is to define the pressure-flow (PQ curve) past piston rings for a known oil and temperature. This is a Fluid-Structure Interaction problem (FSI).

Coding on a Saturday Night

programming

Sitting here. Learning CLion IDE. Learning C++. Installing Rust. Checking the Julia Micro-Benchmarks to see where the languages are at https://julialang.org/benchmarks/.

A Comparison Between Differential Equation Solver Suites

simulation

math

Wow! The below article is must read if you solve differential equations on a regular basis.

Comsol is Great

FEA

CAE

simulation

Definitely one of my favorite CAE programs is Comsol. I will tell you why. But first, some background. I have used a lot of CAE software, to make a short list:

Simerics Pumplinx Hex Mesh Tutorial

CFD

CAE

simulation

Simerics Pumplinx sometimes doesn’t do a a good job in the help describing certain task such as Hex template meshing. Here is some graphics that may help.

World’s Toughest Mudder 2016: A Cautionary Tale

running

endurance

obstacle-course-racing

ultramarathon

mudder

by Jason Nicholson and Molly Kenneth FNP-C

Six Myths of Polynomial Interpolation and Quadrature

math

I found a profound paper written by Professor Lloyd N. Trefethen entitled Six Myths of Polynomial Interpolation and Quadrature. This paper is profound because it goes…

Creating a Custom Header in Wordpress

programming

I used an image for header that I wanted to cite the photographer with a link to his website. There isn’t a clear way to do this in Wordpress tools. Therefore, I searched…

Transmission Line Method

computing

Transmission Line Method (TLM) or Transmission Line Matrix method is an elegant technique used to solve lossless or lossy wave equations. Here I am gathering together…

My Introduction to Computational Fluid Dynamics (CFD)

CFD

CAE

simulation

I have been doing a lot of CFD lately. I have quickly learned that the information one can gain from CFD is far more insightful to the physicals then 0D, lumped parameter…

Differential Algebraic Equations (DAE’s)

math

Often Ordinary Differential Equations (ODE’s) are studied in engineering, especially system dynamics and control theory. However, there are many cases where the system is…

A Good Nerd Laugh

computing

Donald Knuth wrote the program tex (pronounced tek). He cares about code correctness and therefore gave out a reward if you ever found a bug in tex. In 36 years, only 1289…